Let us briefly recall some results about the enumeration of truncated quadrangulations.
Denote the set of all truncated quadrangulations with \(n\)  inner faces and boundary length \(p\)  by \(\mathbb {Q}^{\text{tr}}_{n,p}\) .
[1]} gives an explicit expression for the generating function of truncated quadrangulations:


U(x,y) def=n >0, p>0 #Qtrn,p xn yp
